diff --git a/doc/docs/Python_Tutorials/Cylindrical_Coordinates.md b/doc/docs/Python_Tutorials/Cylindrical_Coordinates.md
index ae4343965..ccc9e82b8 100644
--- a/doc/docs/Python_Tutorials/Cylindrical_Coordinates.md
+++ b/doc/docs/Python_Tutorials/Cylindrical_Coordinates.md
@@ -899,7 +899,7 @@ In principle, computing extraction efficiency first involves computing the radia
 To compute the radiation pattern $P(\theta, \phi)$ requires three steps:
 
 1. For each simulation in the Fourier-series expansion ($m = 0, 1, ..., M$), compute the far fields $\vec{E}_m$, $\vec{H}_m$ for the desired $\theta$ points in the $rz$ ($\phi = 0$) plane, at an "infinite" radius (i.e., $R \gg \lambda$) using a [near-to-far field transformation](../Python_User_Interface.md#near-to-far-field-spectra).
-2. Obtain the *total* far fields at these points, for a given $\phi$ by summing the far fields from (1): $\vec{E}_{tot}(\theta, \phi) = \vec{E}_{m=0}(\theta)e^{im\phi} + 2\sum_{m=1}^M \Re\{\vec{E}_m(\theta)e^{im\phi}\}$ and $\vec{H}_{tot}(\theta, \phi) = \vec{H}_{m=0}(\theta)e^{im\phi} + 2\sum_{m=1}^M \Re\{\vec{H}_m(\theta)e^{im\phi}\}$.  Note that $\vec{E}_m$ and $\vec{H}_m$ are generally complex, and are conjugates for $\pm m$.
+2. Obtain the *total* far fields at these points, for a given $\phi$ by summing the far fields from (1): $\vec{E}_{tot}(\theta, \phi) = \vec{E}_{m=0}(\theta) + 2\sum_{m=1}^M \left(\Re\left[\vec{E}_m(\theta)\right]\cos(m\phi) - \Im\left[\vec{E}_m(\theta)\right]\sin(m\phi)\right)$ and $\vec{H}_{tot}(\theta, \phi) = \vec{H}_{m=0}(\theta) + 2\sum_{m=1}^M \left(\Re\left[\vec{H}_m(\theta)\right]\cos(m\phi) - \Im\left[\vec{H}_m(\theta)\right]\sin(m\phi)\right)$.  Note that $\vec{E}_m$ and $\vec{H}_m$ are generally complex for $m \neq 0$, and are conjugates for $\pm m$.
 3. Compute the radial Poynting flux $P_i(\theta_i, \phi)$ for each of $N$ points $i = 0, 1, ..., N - 1$ on the circumference using $\Re\left[\left[\vec{E}_{tot}(\theta_i, \phi) \times \vec{H}^*_{tot}(\theta_i, \phi)\right]\cdot\hat{r}\right]$.
 
 However, if you want to compute the extraction efficiency within an angular cone given $P(\theta) = \int P(\theta, \phi) d\phi$, the calculations simplify because the cross terms in $\vec{E}_{tot} \times \vec{H}^*_{tot}$ between different $m$'s integrate to zero when integrated over $\phi$ from $0$ to $2\pi$.  Thus, one can replace step (2) with a direct computation of the powers $P(\theta)$ rather than summing the fields.  As a result, the procedure for computing the extraction efficiency within an angular cone for a dipole source at $r > 0$ involves three steps: